Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras

We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the m...

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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2019
Автори: Fujiwara, S., Gyoda, Y.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2019
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/210182
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras / S. Fujiwara, Y. Gyoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210182
record_format dspace
spelling Fujiwara, S.
Gyoda, Y.
2025-12-03T14:28:20Z
2019
Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras / S. Fujiwara, Y. Gyoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 13F60
arXiv: 1808.02156
https://nasplib.isofts.kiev.ua/handle/123456789/210182
https://doi.org/10.3842/SIGMA.2019.040
We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the F-polynomials called the F-matrices and show that the F-matrices have self-duality, which is analogous to the duality between the C- and G-matrices.
The authors are grateful to Professor Tomoki Nakanishi for useful comments and advice. We also thank Toshiya Yurikusa for insightful comments about the principal extension. We would also like to express our gratitude to the referees.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
spellingShingle Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
Fujiwara, S.
Gyoda, Y.
title_short Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
title_full Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
title_fullStr Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
title_full_unstemmed Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
title_sort duality between final-seed and initial-seed mutations in cluster algebras
author Fujiwara, S.
Gyoda, Y.
author_facet Fujiwara, S.
Gyoda, Y.
publishDate 2019
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the F-polynomials called the F-matrices and show that the F-matrices have self-duality, which is analogous to the duality between the C- and G-matrices.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210182
citation_txt Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras / S. Fujiwara, Y. Gyoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ.
work_keys_str_mv AT fujiwaras dualitybetweenfinalseedandinitialseedmutationsinclusteralgebras
AT gyoday dualitybetweenfinalseedandinitialseedmutationsinclusteralgebras
first_indexed 2025-12-07T21:24:39Z
last_indexed 2025-12-07T21:24:39Z
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